Managing Editor: Bruinier, Jan Hendrik
Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna
IMPACT FACTOR 2018: 0.867
CiteScore 2018: 0.71
SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964
Mathematical Citation Quotient (MCQ) 2017: 0.67
On Courant's nodal domain theorem
We study the validity of Courant's nodal domain theorem for eigenfunctions of selfadjoint second order elliptic operators with low regularity assumptions on the coefficients. We prove that in two dimensions Courant's theorem holds also when the coefficients are just bounded and measurable. In the higher dimensional case, we prove a weakened version of Courant's theorem when the coefficients in the principal part are Hölder continuous.
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